This invention relates to a method and apparatus for utilizing coherent backscattering to measure characteristics of a sample and to control a manufacturing process in response to the measured characteristic.
Various optical methods have been employed to measure the size or concentration of particles in some form of suspension. These include microscopic inspection of the sample, determination of the extinction coefficient, turbidity, dissymmetry and bulk light scattering in the forward direction.
Light scattering methods are attractive, as they are noninvasive, only optical access to the sample being required. However, bulk light scattering requires low concentration suspensions, as the light must be able to propagate through the sample. In many cases this necessitates dilution, which is time-consuming and which may, in itself, unpredictably alter the properties to be measured.
Other methods such as sieving, membrane permeation, centrifugation and sedimentation not only require a test sample to be drawn from the bulk sample, but also by their nature they inherently require significant time to perform, typically ranging from tens of minutes to hours. It is thus not possible to incorporate these methods into a process control function.
The present invention makes use of coherent backscattering to determine characteristics of the sample. Not only is the method disclosed noninvasive, but it works well on non-dilute suspensions and even opaque materials, and requires, at most, a few minutes to perform.
Electromagnetic radiation or light incident on a sample from a direction A may scatter into an arbitrary direction B (FIG. 1). For dilute samples, the scattered light detected in direction B will have experienced only a single scattering event within the sample. Such dilute samples will not exhibit the coherent backscattering phenomenon.
If the sample is non-dilute, the scattered light detected in direction B may have experienced several scattering events within the sample. FIG. 2 shows three such trajectories which contribute to the light detected in direction B. One trajectory arises from the ray 1, in direction A, which undergoes one scattering event and is redirected along the ray 2. A second trajectory arises from the same ray 1, which undergoes three scattering events, ultimately redirected along the ray 3. A third trajectory arises from the ray 4, in direction A, which undergoes one scattering event and is also redirected along the ray 3.
As the path lengths of these trajectories are uncorrelated, the phases associated with these trajectories are uncorrelated. The total light detected in the arbitrary direction B, being the sum over all such possible trajectories, exhibits no special interference effect, since the uncorrelated phases average out.
However, a special interference phenomenon may occur when the direction B is at (or near) incident direction A. In this case, the trajectories always occur in pairs (one being the time-reverse of the other), where each member of the pair possesses identical path length. The phases associated with these time-reversed trajectories are thus identical, and these two trajectories always constructively interfere.
FIG. 3 shows two such trajectories. The first trajectory arises from the ray 5, in direction A, which undergoes three scattering events and is redirected (ray 6) in direction B. The second trajectory arises from the ray 7, in direction A, which undergoes the same three scattering events (but in reverse order) and is redirected (ray 8) in direction B. The only difference between these two trajectories is their direction with respect to time (i.e. the sequence of their scattering events); the path length of these two trajectories is identical. Thus these two paths always constructively interfere. Furthermore, every trajectory from incident direction A, which scatters within the sample and ultimately is redirected to the backscattering direction B, has such a time-reversed trajectory with identical path length. Hence, every such path has a time-reversed path with which it constructively interferes. The observed intensity scattered into the backscattered direction B is thus enhanced, by this constructive interference effect, above its classical value.
If coherent backscattering occurs in a sample, the increased intensity occurs not only at the incident angle, but also, to a reduced degree, within some angle off the incident angle. The range of the angle in which the effect occurs is called the line width of the coherent backscattering and the coherent backscattering intensity as a function of the angle is referred to as the line shape.
This line width, .DELTA..theta., is a function of the scattering mean-free-path, L, of light in the random medium. In the case where L is very much greater than .lambda., the wavelength of the light in the sample, .DELTA..theta. is on the order of .lambda./L both for liquid suspensions (e.g., polystyrene spheres in water) and, under special conditions, for particulate solids (e.g., network of colloidal SiO.sub.2, or BaSO.sub.4 microparticles).
The mean-free-path is, in turn, a function of the size and concentration of scatterers in the sample. In the above examples, L=1/n.sigma., where n is the number density of scatterers and .sigma. is the relevant elastic scattering cross-section of a single scatterer. It is thus possible to obtain this elastic scattering cross section, .sigma., for a given concentration of scatterers by measuring the mean-free-path, L, in coherent backscattering. Similarly, it is possible, if this elastic scattering cross section is known, to obtain the concentration of scatterers by measuring the mean-free-path, L, in coherent backscattering. Since the elastic scattering cross section is a known (usually previously measured) function of the size of the scatterer, it is thus possible to obtain the particle size for a given concentration of scatterers or the concentration for a given size scatterer by measuring the mean-free-path, L, in coherent backscattering.
While, even for monodisperse, well-characterized samples, it has proved difficult to calculate the relevant elastic scattering cross section, as a function of the particle size from first principles, where this is needed, this can be measured on test samples. Nonetheless, the relationship, L=1/n.sigma., still obtains. For polydisperse samples, the relevant elastic scattering cross section also depends on some moment of the distribution in particle size, and again one would perform calibration experiments. Similarly, if the scatterers are nonspherical, one does not calculate the relevant scattering cross section but, rather, performs calibration experiments.
Again, for most applications, while L=1/n.sigma., the theoretical dependence of the relevant elastic scattering cross section, .sigma., on the particle size is unknown. Nevertheless, as disclosed herein, coherent backscattering and its associated line shape can often be observed and measured.